Gutt, S. An explicit *-product on the cotangent bundle of a Lie group. (English) Zbl 0522.58019 Lett. Math. Phys. 7, 249-258 (1983). Summary: We give explicit formulas for a *-product on the cotangent bundle \(T^*G\) of a Lie group \(G\); these formulas involve on the one hand the multiplicative structure of the universal enveloping algebra \(U(\mathfrak g)\) of the Lie algebra \(\mathfrak g\) of \(G\) and on the other hand bidifferential operators analogous to the ones used by Moyal to define a *-product on \(\mathbb R^{2n}\). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 12 ReviewsCited in 76 Documents MSC: 53D55 Deformation quantization, star products 53B50 Applications of local differential geometry to the sciences 22E46 Semisimple Lie groups and their representations Keywords:deformation of algebra of functions; Moyal product; Weyl transform; hydrogen atom; deformations on orbits of semisimple Lie groups PDF BibTeX XML Cite \textit{S. Gutt}, Lett. Math. Phys. 7, 249--258 (1983; Zbl 0522.58019) Full Text: DOI OpenURL References: [1] Bateman, H., Higher Transcendental Functions (1953) p. 38. · Zbl 0051.34703 [2] BayenF., FlatoM., FronsdalC., LichnerowiczA., and SternheimerD., Ann. Phys. 111, 61-151 (1978). · Zbl 0377.53024 [3] CahenM. and GuttS., Lett. Math. Phys. 6, 395-404 (1982). · Zbl 0522.58018 [4] Dixmier, J., Universal Enveloping Algebra (1978) p. 96. [5] GerstenhaberM., Ann. Math. 79, 59-103 (1964). · Zbl 0123.03101 [6] LichnerowiczA., Lett. Math. Phys. 2, 133-143 (1977). · Zbl 0392.58019 [7] MoyalJ., Proc. Cambridge Phil. Soc. 45, 99-124 (1949). [8] VeyJ., Comm. Math. Helv. 50, 421-454 (1975). · Zbl 0351.53029 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.